When the objective function \(g\)  is not convex, the convergence of the trajectories generated by (HBS) is a largely open question. Recent progress has been made in [1]}, where the convergence of the trajectories of a system, which can be considered as a perturbation of (HBS) has been obtained in a non-convex setting.
For other results concerning the dynamical system (HBS) and its extensions we refer to [2]}, [3]}, [4]}.
